Question

For the function f(x) = -(x+6)(x+2), when is the function decreasing and when is it increasing?

Answer 1

Answer:

• The function f is increasing to the left of -4 (-∞ , -4]

• The function f is decreasing to the right  of -4 [-4 , +∞)

Step-by-step explanation:

f(x) = -(x+6)(x+2)

     = -(x² + 2x + 6x + 12)

     = -(x² + 8x + 12)

     = -x² - 8x - 12

The leading coefficient is -1 (the coefficient of the highest term -x² of the trinomial)

Then

The parabola opens downward.

………………………………………

$-\frac{b}{2a} =-\frac{-8}{2\times \left( -1\right) } =-4$

Then

The function f is increasing to the left of -4 (-∞ , -4]

The function f is decreasing to the right  of -4 [-4 , +∞)